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 TOPICS This page:   calculus    Search   Dr. Math See also the Internet Library:   calculus HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Calculus Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Chain rule.     Maximizing the volume of a box.     Maximizing the volume of a cylinder.     Volume of a tank.     What is a derivative? Minimizing the Time to Rescue [11/29/1999] A man is drowning in the water 300 meters down the beach and 100 meters out from where I'm standing. I can run 5 meters/second and swim 3 meters/second... Minimum and Maximum Pollution [04/26/2000] Find the points of minimum and maximum pollution between two plants releasing 60 and 240 ppm of pollution... Minimum, Maximum Value of a Two-variable Function [6/27/1996] Find f min and f max where x and y are real numbers and f(x,y) = 2(sin x)(cos y)+3(sin x)(siny)+6(cos x). Minimum Value Problem [7/14/1995] I need to find the minimum value of E for E = be^(-ar) - dr^(-6) where b, a, and d are constants and r is the variable. Min, Max of 3-Variable Function [8/16/1996] Find all the critical points and determine their nature for the function z = x^3 - 6xy + y^3. Modelling Discrete Data with Exponential Functions [5/14/1996] How can I fit an exponential function to a set of three discrete data points? Monkey Climbing a Chain [09/22/1999] A 20-lb. monkey is attached to a 50-ft. chain that weighs 0.5 lb. per (linear) foot... The Monotone Convergence Theorem [10/02/1998] Could you please explain the meaning and purpose of the monotone convergence theorem? Moving a Circle on a Polar Graph [05/04/2001] How do you move a circle so the center is not (0,0), but to where the center can be (r,[theta])? Moving Particle [07/14/1999] Assume a particle moves on the x-axis according to the formula x = t^ 3- 6t^2+9t+5. Find: the velocity when t = 3... The Moving Shadow [03/24/1999] A man walks toward a light... at what rate does the tip of his shadow move and at what rate does its length change? Multidimensional Calculus and Vector Geometry [02/09/1999] The depth of iron ore can be approximated by a plane... Navigation Formula [10/14/1996] Given the starting latitude, longitude, distance, and course of a plane, what formula gives its destination latitude and longitude? Newton-Raphson Method [02/28/2000] How can I find the 1st, 2nd, 3rd iterations and the parameters of x^3 - 13.1x^2 + 48.48x - 46.62 using the Newton-Raphson method? Newton-Raphson Method [06/24/2009] Are there any equations that cannot be solved using the Newton-Raphson method, regardless of the initial estimate? Newton's Method and Square Roots [12/04/1998] Can you explain how finding square roots by hand relates to Newton's method for approximating the zero of a function? Non-Constant Functions [02/12/2001] Are there any non-constant functions f and g such that (f*g)' = f'*g'? Nondifferentiable Functions [11/6/1994] In my calculus book, it mentions a function that is not differentiable at any point due to the fact that it is not smooth at any point. It does not go any farther, and I was interested in hearing more. Non-Linear Equation [2/13/1996] Solve 5x^2 + log(x) = 0 for x... Nonvertical Asymptotes [10/16/2001] Does this problem have slant asymptotes? f(x)=(x^(4/3)+x^(1/3)-2)/(x^ (4/3)-16). I'm also having trouble taking the derivative of this problem: f(x)=((x^2(x+1))-(1-x))^(1/2). A Norman Window [1/16/1995] A Norman window is a window in the shape of a rectangle with a semicircle attached to the top. Assuming that the perimeter of the window is 12 feet, find the dimensions that allow the maximum amount of light to enter. The N Targets Problem [11/15/2001] Given n targets with equal probability of being hit by a cannon, that is, 1/n. Let X be the number of firings required to hit all the targets. What is the expectation E(X) of X? Numeric Derivatives Using TI-83, TI-92 [10/17/2003] My calculator says that the numeric derivative of sin(x) is sin(2x)/(2x). Shouldn't it be cos(x)? Oblique Asymptotes [04/03/2002] I'm stuck on how to calculate oblique limits, for example, x^2/(x-3). Odd Bernoulli Numbers Must Be 0 [02/16/2003] Take the second derivative of t/exp(t) -1 and find that it is an even function; show that an even function, when expressed as a Taylor Series, has only even powers of t; draw the conclusion that the odd Bernoulli numbers have to be 0. ODEs and Integration with the Chain Rule [05/30/1998] What is an ordinary differential equation? How do you integrate f'(x) = (x-1)^4? Oil Can Dimensions [12/11/2001] What are the dimensions of an oil can with a one-liter capacity that uses the least amount of tin? Operating a Tour Service [5/21/1996] How many people does it take to maximize your profit? Optimization [12/13/1995] An AP Calculus student asks questions about his chapter test. Optimization [11/26/1996] To make a funnel, we take a circular piece of metal, cut out a sector, and connect the two radial edges together to make an open cone. What should the angle of the sector be to maximize the volume of the cone? Optimization: Minimum Area [11/07/1997] How do you fold a piece of paper (rect. with width a and unlimited length) so one corner just reaches the righthand side for minimum area? Optimization (Min-Max) [01/21/2001] If a piece of string of fixed length is made to enclose a rectangle, show that the enclosed area is greatest when the rectangle is a square. Optimizing Advertising [10/15/2003] Doubling the amount spent on advertising increases total income by 20 percent. What is the optimum level of advertising? An Ordinary Differential Equation in Everyday Life? [03/26/2011] A student wonders about the real world applicability of ordinary differential equations. Doctor Jordan steps through an example. Ordinary Differential Equation, Second Order [10/26/2002] I've been looking for solutions to the differential equation y'' = x^2 / y^2. Parametric Equations [07/21/1998] A curve is given parametrically by the equations: x = (3-2k)^2 and y = (2+k)^2. Find dy/dx, the x-intercept, the cartesian equation... Partial Derivatives [03/24/2001] What sense do partial derivatives make in the case where u is given as a function of two variables, say x and y...? Partial Fractions [06/08/1997] How do you break 1/x^2*(x+2) into partial fractions? Partial Fractions [11/23/2003] I need to put this fraction into power series formation: (3x^2 - x)/(x^3 - x^2 - x + 1). I've tried to use partial fractions but keep getting stuck. Percentage of Numbers Divisible by 6, 8 [03/18/2003] What percentage of numbers is divisible by 6? by 8? Page: []

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